Khan.scratchpad.disable(); For every level Daniel completes in his favorite game, he earns $490$ points. Daniel already has $450$ points in the game and wants to end up with at least $3740$ points before he goes to bed. What is the minimum number of complete levels that Daniel needs to complete to reach his goal?
To solve this, let's set up an expression to show how many points Daniel will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Daniel wants to have at least $3740$ points before going to bed, we can set up an inequality. Number of points $\geq 3740$ Levels completed $\times$ Points per level $+$ Starting points $\geq 3740$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 490 + 450 \geq 3740$ $ x \cdot 490 \geq 3740 - 450 $ $ x \cdot 490 \geq 3290 $ $x \geq \dfrac{3290}{490} \approx 6.71$ Since Daniel won't get points unless he completes the entire level, we round $6.71$ up to $7$ Daniel must complete at least 7 levels.